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Profile of Keith Moffatt

Farooq Ahmed

Science Writer

Keith Moffatt was born in 1935 and raised in Edinburgh, Scotland. He was four years old when his father left home to serve in the Second World War. “At that age, you accept things,” Moffatt recalls. “It was a time of great shortage. Everything in the UK was rationed—food, clothes, fuel, even sweets!”

The elder Moffatt, an accountant, had introduced his son to mathematical games and arithmetic puzzles, and, when he re- turned at the war’s end in 1945, recreational mathematics recommenced.

The early tutelage had a lasting effect: Moffatt’s facility with numbers would trans- form into an aptitude for applied mathe- matics and its use in fluid mechanics and astrophysics. His contributions to our under- standing of magnetic and spin fields as well as his advocacy for the study of mathematics around the world have earned him fellow- ships in the Royal Societies of both London and Edinburgh. A 2005 recipient of the Royal Society of London’s Hughes Medal, he serves as an emeritus professor of mathematical physics at the University of Cambridge. He was elected as a foreign associate of the National Academy of Sciences in 2008.

Magnetic Fields in a Turbulent Medium

Moffatt completed his undergraduate stud- ies in mathematics at the University of Edinburgh. He left Scotland for Trinity College, Cambridge, in 1957, where he came under the influence of George Batchelor, an Australian fluid dynamicist. Batchelor set Moffatt to work on his first research project and played a decisive role in his career. “George was very sympathetic to students who came from outside Cambridge, as it had been his own career path,” Moffatt explains.

In 1959 Batchelor founded the Depart- ment of Applied Mathematics and Theoreti- cal Physics at Cambridge—a department that counts in its ranks some of the world’s most influential fluid dynamicists and theoretical physicists. He gave Moffatt a prepublication draft of his paper on how turbulence inter- acts with temperature or a contaminant that does not influence the turbulence (1).

Two years later, Moffatt’s first paper in 1961 extended Batchelor’s ideas to the in- teraction of turbulence with a weak magnetic

field and obtained the spectrum of the mag- netic fluctuations (2). The result would be verified experimentally nearly three decades later by French researchers, using liquid gallium and an applied magnetic field (3).

“The application that I had most in mind at that time,” Moffatt notes, “was in astro- physics.” In the 1950s, dynamo theory, which is the study of how the earth, stars, and other heavenly bodies generate and maintain magnetic fields, was beset by conflicting ideas. Furthermore, how these magnetic fields interacted with the interstellar medium and its turbulent ionized gases was poorly understood.

Knotted Vortices

Toward the end of the 1960s, while teaching a course on magnetohydrodynamics, Moffatt identified an integral characteristic of fluid flow that he named “helicity” (4), building on the observations of two scientists working nearly a century apart.

“In 1869 Lord Kelvin recognized the fro- zen property of vortex lines in fluid flows, and in 1958 Lodewijk Woltjer, an astro- physicist then at the University of Chicago, demonstrated the invariance of a puzzling integral quantity in the flow of a perfectly conducting or Euler fluid. In struggling to find a physical interpretation of Woltjer’s invariant, it dawned on me that there must be an analogous result for the nonlinear Euler equations.”

Helicity, as Moffatt explains, represents the degree of linkage or entanglement in a field of vorticity, which can be thought of as the spin associated with a velocity field. Helicity is an invariant of the Euler equations, which govern ideal, nonviscous flows. This concept established a bridge between classical fluid mechanics and topology, the study of shapes and their continuous deformation.

Moffatt gives credit for the finding to Jean- Jacques Moreau, now an emeritus professor in Montpellier, France, who had found the same invariant several years before his pub- lication (5). “As so often happens in our subject,” Moffatt explains, “someone else proved the concept in a paper that was completely buried. Moreau didn’t call it

Keith Moffatt. Photo by Jill Paton-Walsh.

helicity, but the result is there. He and I discovered it quite independently.”


Helicity had immediate applications in dy- namo theory, and especially for the expla- nation of the earth’s magnetic field. About halfway to the center of the earth, the mantle gives way to a liquid metal core, “a con- ducting fluid in random motion superposed on differential rotation,” Moffatt explains. This combination generates a magnetic field. He showed that dynamo action occurs even in a weakly conducting fluid, provided the fluid domain is large enough and the turbu- lence has an average nonzero helicity (6).

While on a sabbatical at the Université Pierre et Marie Curie in Paris, Moffatt wrote the first monograph on dynamo theory, in- corporating helicity and its implications for planetary and astrophysical dynamos (7). “By the late 1970s,” he notes, “the basic principles were well established, so the time was ripe for such a book, which is still a standard in- troductory text.” The publication led to an explosion of activity in the field of dynamo theory, with three other books on the subject produced across the world within the next five years. A massive computational effort throughout the 1980s and 1990s followed. Moffatt is currently working on an updated version of the monograph.

This is a Profile of a recently elected member of the National Academy of Sciences to accompany the member’s Inaugural Article on page 3663.

3650–3652 | PNAS | March 11, 2014 | vol. 111 |

no. 10

Image | Keith Moffatt

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